Pull Apart Educational Model
So here is how you would do this using game logic. (The blend file at the end if you want to skip my explanation).

1) Connect an Always sensor to a Mouse actuator (the default state of this actuator is to make the mouse visible so you shouldn't have to change anything).

2) Where the yellow box is add a Boolean property and make sure it's starting state is True (checked).

3) Add two mouse sensors (as seen in the light blue box). Set one to Mouse Over and the other to Left Button. Connect both sensors to the same controller and make sure it is set to Add (that is the default). Now connect the Add controller to a Property actuator set to toggle the property you created in step 2 (see the dark blue box).

4) Add a Property sensor and set it to Equal "True" then connect it to a Visibility actuator in which Visible is checked.

5) Add a Property sensor and set it to Equal "False" then connect it to a Visibility actuator in which Visible is unchecked and Occlusion is checked.